It took a few days, but now the cops are launching an official investigation according to TMZ.

Law enforcement sources tell TMZ … a senior investigator for the L.A. County D.A.’s Bureau of Investigation contacted Shelly Sterling Tuesday … asking for an interview in connection with the extortion investigation.

Donald Sterling gave an interview last week … telling a magazine, “I wish I had just paid her off.”

Stiviano’s people told us a week ago … Sterling called her after we posted the audio … asking her, “How can we make this go away?” We have since learned it was NOT Sterling who initiated the call — it was Stiviano.